{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#本章需导入的模块\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.rcParams['font.sans-serif']=['SimHei']  #解决中文显示乱码问题\n",
    "plt.rcParams['axes.unicode_minus']=False\n",
    "import warnings\n",
    "warnings.filterwarnings(action = 'ignore')\n",
    "from sklearn.metrics import confusion_matrix,f1_score,roc_curve, auc, precision_recall_curve,accuracy_score\n",
    "from sklearn.model_selection import train_test_split,KFold,LeaveOneOut,LeavePOut # 数据集划分方法\n",
    "from sklearn.model_selection import cross_val_score,cross_validate # 计算交叉验证下的测试误差\n",
    "from sklearn import preprocessing\n",
    "import sklearn.linear_model as LM\n",
    "from sklearn import neighbors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(123)\n",
    "N=100\n",
    "x=np.linspace(-10,10, num=N)\n",
    "y=14+5.5*x+4.8*x**2+0.5*x**3\n",
    "z=[]\n",
    "for i in range(N):\n",
    "    z.append(y[i]+np.random.normal(0,50))\n",
    "\n",
    "fig,axes=plt.subplots(nrows=1,ncols=2,figsize=(10,4))\n",
    "axes[0].scatter(x,z,s=10)\n",
    "axes[0].plot(x,y,'k-',label=\"真实关系\")\n",
    "modelLR=LM.LinearRegression()\n",
    "X=x.reshape(N,1)\n",
    "Y=np.array(z)\n",
    "modelLR.fit(X,Y)\n",
    "axes[0].plot(x,modelLR.predict(X),linestyle='--',label=\"线性模型\")\n",
    "linestyle=[':','-.']\n",
    "degree=[2,3]\n",
    "for i in range(len(degree)):\n",
    "    tmp=pow(x,degree[i]).reshape(N,1)\n",
    "    X=np.hstack((X,tmp))\n",
    "    modelLR.fit(X,Y)\n",
    "    axes[0].plot(x,modelLR.predict(X),linestyle=linestyle[i],label=str(degree[i])+\"项式模型\")\n",
    "KNNregr=neighbors.KNeighborsRegressor(n_neighbors=5)\n",
    "X=x.reshape(N,1)\n",
    "KNNregr.fit(X,Y)\n",
    "axes[0].plot(X,KNNregr.predict(X),linestyle='-',label=\"复杂模型\")\n",
    "axes[0].legend()\n",
    "axes[0].set_title(\"真实关系和不同复杂度模型的拟合情况\")\n",
    "axes[0].set_xlabel(\"输入变量\")\n",
    "axes[0].set_ylabel(\"输出变量\")\n",
    "\n",
    "X=x.reshape(N,1)\n",
    "Y=np.array(z)\n",
    "modelLR.fit(X,Y)\n",
    "np.random.seed(123)\n",
    "k=10\n",
    "scores = cross_validate(modelLR,X,Y, scoring='neg_mean_squared_error',cv=k, return_train_score=True)\n",
    "MSEtrain=[-1*scores['train_score'].mean()]\n",
    "MSEtest=[-1*scores['test_score'].mean()]\n",
    "degree=[2,3]\n",
    "for i in range(len(degree)):\n",
    "    tmp=pow(x,degree[i]).reshape(N,1)\n",
    "    X=np.hstack((X,tmp))\n",
    "    modelLR.fit(X,Y)\n",
    "    scores = cross_validate(modelLR,X,Y, scoring='neg_mean_squared_error',cv=k, return_train_score=True)\n",
    "    MSEtrain.append((-1*scores['train_score']).mean())    \n",
    "    MSEtest.append((-1*scores['test_score']).mean())\n",
    "        \n",
    "KNNregr=neighbors.KNeighborsRegressor(n_neighbors=5)\n",
    "X=x.reshape(N,1)\n",
    "KNNregr.fit(X,Y)\n",
    "scores = cross_validate(KNNregr,X,Y, scoring='neg_mean_squared_error',cv=k, return_train_score=True)\n",
    "MSEtrain.append((-1*scores['train_score']).mean())\n",
    "MSEtest.append((-1*scores['test_score']).mean())\n",
    "\n",
    "axes[1].plot(np.arange(1,len(degree)+3),MSEtrain,marker='o',label='训练误差(10折交叉验证法)',linestyle='--')\n",
    "axes[1].plot(np.arange(1,len(degree)+3),MSEtest,marker='*',label='测试误差(10折交叉验证法)')\n",
    "\n",
    "axes[1].legend()\n",
    "axes[1].set_title(\"不同复杂度模型的训练误差和测试误差(Err)\")\n",
    "axes[1].set_xlabel(\"模型复杂度\")\n",
    "axes[1].set_ylabel(\"MSE\")\n",
    "fig.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "说明：\n",
    "1、利用通过数据模拟，直观展示模型的过拟合，以及过拟合模型下的训练误差和测试误差的特点。\n",
    "2、这里，复杂模型为K近邻法建立的预测模型，是一种典型的非线性模型。具体内容详见第4章。\n",
    "3、对不同复杂度模型，利用cross_validate()计算10折交叉验证下的训练误差和测试误差。随模型复杂度的提高，训练误差单调下降，测试误差呈先下降后来上升的U字形。显然，复杂模型的训练误差最小但测试误差并非最小，出现了模型的过拟合。\n",
    "4、scores['train_score']为训练误差，scores['test_score']为测试误差。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x17de5f66a88>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,axes = plt.subplots(1,2,figsize=(10,4))\n",
    "modelLR=LM.LinearRegression()\n",
    "X=x.reshape(N,1)\n",
    "Y=np.array(z)\n",
    "modelLR.fit(X,Y)\n",
    "np.random.seed(123)\n",
    "k=10\n",
    "scores = cross_validate(modelLR,X,Y, scoring='neg_mean_squared_error',cv=k, return_train_score=True)\n",
    "fdata=pd.Series(-1*scores['test_score'])\n",
    "axes[0].boxplot(x=fdata,sym='rd',patch_artist=True,boxprops={'color':'blue','facecolor':'pink'},labels ={\"线性模型\"},showfliers=False) \n",
    "MSEMedian=[np.median(-1*scores['test_score'])]\n",
    "MSEVar=[(-1*scores['test_score']).var()]\n",
    "MSEMean=[(-1*scores['test_score']).mean()]\n",
    "\n",
    "degree=[2,3]\n",
    "lab=['二项式模型','三项式项模型']\n",
    "for i in range(len(degree)):\n",
    "    tmp=pow(x,degree[i]).reshape(N,1)\n",
    "    X=np.hstack((X,tmp))\n",
    "    modelLR.fit(X,Y)\n",
    "    scores = cross_validate(modelLR,X,Y, scoring='neg_mean_squared_error',cv=k, return_train_score=True)\n",
    "    fdata=pd.Series(-1*scores['test_score'])\n",
    "    axes[0].boxplot(x=fdata,sym='rd',positions=[i+2],patch_artist=True,boxprops={'color':'blue','facecolor':'pink'},labels ={lab[i]},\n",
    "                    showfliers=False) \n",
    "    MSEMedian.append(np.median(-1*scores['test_score']))\n",
    "    MSEVar.append((-1*scores['test_score']).var())\n",
    "    MSEMean.append((-1*scores['test_score']).mean())\n",
    "\n",
    "KNNregr=neighbors.KNeighborsRegressor(n_neighbors=5)\n",
    "X=x.reshape(N,1)\n",
    "KNNregr.fit(X,Y)\n",
    "scores = cross_validate(KNNregr,X,Y, scoring='neg_mean_squared_error',cv=k, return_train_score=True)\n",
    "fdata=pd.Series(-1*scores['test_score'])\n",
    "axes[0].boxplot(x=fdata,sym='rd',positions=[4],patch_artist=True,boxprops={'color':'blue','facecolor':'pink'},labels ={\"复杂模型\"},\n",
    "                showfliers=False) \n",
    "MSEMedian.append(np.median(-1*scores['test_score']))\n",
    "MSEVar.append((-1*scores['test_score']).var())\n",
    "MSEMean.append((-1*scores['test_score']).mean())\n",
    "\n",
    "axes[0].plot(np.arange(1,5),MSEMedian,marker='o',linestyle='--')\n",
    "axes[0].set_ylabel('MSE')\n",
    "axes[0].set_xlabel('复杂度')\n",
    "axes[0].set_title('不同复杂度模型下的Err(10折交叉验证法)')\n",
    "axes[0].grid(linestyle=\"--\", alpha=0.3)\n",
    "\n",
    "axes[1].plot(np.arange(1,5),preprocessing.scale(MSEMean),marker='o',linestyle='-',label=\"Err\")\n",
    "axes[1].plot(np.arange(1,5),preprocessing.scale(MSEVar),marker='o',linestyle='--',label=\"方差\")\n",
    "axes[1].grid(linestyle=\"--\", alpha=0.3)\n",
    "\n",
    "axes[1].set_title('不同复杂度模型测试误差的期望(Err)与方差变化趋势图')\n",
    "axes[1].set_xlabel('复杂度')\n",
    "axes[1].set_ylabel('标准化值')\n",
    "plt.legend(loc='best', bbox_to_anchor=(1, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "说明：\n",
    "1、对于上述模拟数据和四种复杂度模型，利用箱线图展示了10折交叉验证下各折测试误差的统计分布。简单模型预测误差大，表现出测试误差箱线图的中位数线偏高，均值大，且箱体宽方差较大。随着复杂度增加情况相应发生改变。\n",
    "2、boxplot()画箱线图时可以指定多个箱体在图中的位置（positions），箱体是否填充色（patch_artist=True），并以数据字典方式指定箱体边框颜色（'color':'blue'）填充色（'facecolor':'pink')，箱体标签（labels）以及是否显示数据中的异常点（showfliers）等。 \n",
    "3、preprocessing.scale()是对数据进行标准化处理，即数据减去均值除以标准差。处理后的数据均值等于0标准差等于1。通过标准化处理实现将不同数量级的数据变动趋势画在同一幅图中。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TAPiXKj9KpSb0Q3dano4OqE+jS3unG+fuCWCJiAxHlxI/QXdYbxORk9Adu13QAXWSiJyNDs4fewKJYf9n6NrWrcb3OHS/jqdpBhFpjw4cfwHDlVL5xvbb0cMcfWtQoH11tVLqGzFeWvM0XaHb5Aca+680jokRSBYCtyql8oxtSeiazIX4nOM62APaj77NR/ONfQRwGoWdPf47iR69V4ge838M+sHa1yhs7FNlR+/Y0EOfdxr7utE1Xw/TgZ0ich+6c/gkdHPdo0bh6Drf/AzbUny+d0GPvhoKjJbDJbph6D4Sf70AKKXeFJHF6GuhL2Vrwp73H8ITFQbjYq34h25PPKmS33ajH4oV/TYKfYPPMr4LunT+ObrJYzG6pDkKmI0OGNvQQeBo9EP+DJ/8JgAZGOOnjW1xwAjj/wvRD7ah6FLvEuAL9ANrHjpYfIl+uLXxyeMH9OiVF430A31+O8Ow6Qx0p/VWdJDx/P2GLtX5btsIXGbsfxWHx533A7oZ/7cG3keXwJqY4DPPy2tD0A+leUCaz+829IOtH3qE1R1G+vXoB+YYjHczjLQXGX45zyePT4GjjP+3GOkaGX4+CT3csS86SPwDOBYdqDznaYeRxvN9M+XfJZkOXOvzvbPP/42MY8Yb19NFfvveim76WOTn71rbg34gNvfYABxj/J+EDkb3Aq2NbbHGufnLuJ5uQr+/EoduAnsP3V+VBbTysesS4Hmf78ejmzW3GH/fGscegu7v86Q7DXgNfR2vRwfAPej+sMnows1S47cbgURjv3gj3w3AP/zO3ftGPmur+Cvx5BWuf54LOEqYUFHVUvSUC/nADnW49Of7exy6Q2yT/++iRyPZlR4HXtkxY9E3YD9gjSo/vr4T0FWV7+BF9Jjucs0klbQvRwwi0lGV73upLG1AmgOM5hlRZd/WNQ05/JZuWCB6KPUBVfHIJU+axqrqZqSq8q9sVFSFb0uLSKKqxZvHot+6Lwinc1oXokEhSpQoUaJ4iU6IFyVKlChRvESDQpQoUaJE8RLxo4+aNWumOnToUKd93W43Nps14mJUS/hhFR0Q1RKO1FfHmjVrMpRSzf23R3xQ6NChA6tX+79UWTNKS0uJja3VVOxhS1RL+GEVHRDVEo7UV4eIVPQyZsNuPnI6w3qywloR1RJ+WEUHRLWEI2bpaNBBIT8/P9QmBIyolvDDKjogqiUcMUtHgw4KUaJEiRKlLA06KCQlJYXahIAR1RJ+WEUHRLWEI2bpaNBBwQqdTR6iWsIPq+iAqJZwxCwdDTMorF8AT/QmZmZzeKK3/h7hOByO6hNFCFbRYhUdENUSTnzwyx6GPPQl3aZ+zpCHvuSDX8rNKVgvIn5Iaq1ZvwA+vglKC/V0lI6/9HeAvuOr2jNKlChRQsoHv+zh3+9voLBUT4+151Ah/35/AwDjjmlT1a41puHVFP53P5T6zXFVWqi3RzBWqRKDdbRYRQdEtYQLj3621RsQPBSWunj0s62V7FF7Gl5QcFSyKFNl2yOElJSU6hNFCFbRYhUdENUSLuw9VPGkrZVtrwsNLyiktK3d9gghMzOz+kQRglW0WEUHRLWEC0ekJtZqe11oeEFh+DSI9TuBYtfbIxgrTYFuFS1W0QFRLeHChMFHltuWGGvnjtP8F2usOw0vKPQdD2c9BSntUAjEp4ByQVyjUFtWL3zWfY54rKLFKjogqiUcKHW5WbphP8lxdlqlJCBAm9RE/nNOn4B1MkNDHH0EOjD0Ha9HHzlL4L0rISk91FbVi6ZNm4bahIBhFS1W0QFRLeHAc8u3s2GPg+cu6c/oPq1NO07Dqyn44HA4ICYOLpgPRw4OtTn1ItLHXvtiFS1W0QFRLaHm1z0Onv5yG2cffYQ3IJilo0EHhdJSn+VaSwrgs8mwa2XoDKoHZbREOFbRYhUdENUSSoqdLiYtWEd6chz3je3l3W6WjgYdFMqiYPPH8NFN5d9jiBIlSpQQ8eQX29j6dy4PnduH1KQ404/XoINCmfHKcclw1mzI2g5fPxw6o+pIJI+99scqWqyiA6JaQsXPf2bz4tfbuWBgO07t3rLMb2bpaJBBYcmOJYxaNIoBbw1g1KJRLNmxRP/Q+RQ4egKsegr2rQutkbUk0qrEVWEVLVbRAVEtoaCwxMXtC9bROiWRKWf2KPd7tPkoQCzZsYTp305nX/4+FIp9+fuY/u30w4HhtBmQ3AyW3A4RNJ65oKAg1CYEDKtosYoOiGoJBY98toUdGfk8cl5fGieUn5rDLB0Nbkjq7J9nU+QqKrOtyFXE7J9nM6bTGEhMg3PnQOPWEKHjmaNUTGlpKbt376aoqKj6xAHA5XJx8ODBoBwrISGBtm3bRvS8PlEO8932TF5ZtYuJx7dnSJdmQT12gwsK+/P3V7+949DD/5fk6/6GMCc5OfxtrClmadm9ezeNGzemQ4cOQXmBye12Y7OZXxlXSpGZmcnu3bvp2LGjKceIXl/BI6/YyR2L1tGhaRJ3ndG90nRm6Qh685GItBSRb6r4vY2I7BaRr4y/5oE8fqvkVhVub5ncsvzGD/8Fb44HtzuQJphCTIx14rtZWoqKimjatGnEvtFaGSJC06ZNTa0BRa+v4DFzyWb2HCpk1vn9SIqr3FazdAQ1KIhIGvAaUFWIOw6YqZQaZvwFtP59c/+bSbAnlNueFpdGiauk7Ma2g+CPlfDza4E0wRQi8YWcyjBTSzADgsvlqj5RgDBbV/T6Cg5f/3aQt3/8k2tO6sTADlXPsmCVl9dcwAVAThVpBgNXicjPIvJgoA0Y02kM00+YTuvk1ghC6+TWjOs8js3Zm5n01SRKXT49+v0vgw4nwbJpkLM30KZEiVLt5Gy+N/6BAwfMNidKCHEUlHLXovV0bdGIW0d2C5kdQa1HKaVyoNpSzSfAA0AB8IWI9FVKrfdNICLXANcAtGvXjoyMDEC3scXExHhvpLi4OBo3buydKtdms5Gens6JTU/kuGHHUVBQwBFHHEFxcTHtE9oze+NsbvnyFh458REK8/ULbAmnPkjy6yMp+e+N5I5+AZvdTnp6OocOHcLpdAKQlpZGYWGht/reqFEjRITc3FydR0ICSUlJZGVlAWC320lLSyM7O9tbmkxPT6egoMCbR+PGjVFKkZeX580jMTGR7OxsQFcdU1NTycrKwu12U1BQgNvtJj8/n+LiYgCaNGmCy+UiPz8fgMTEROLj4zl06BCgFxtJSUnx5gF6Xpjc3FxKSnStKSUlBafT6c0jKSmJ2NhY7zn25JGZmYlSytuU4XA4vEPmUlJSKC0t9Y6WqM5PhYX63PvmkZqaSnFxsfe35ORk7HY7OTm6fBEfH09ycrL3HHt87esnpRQul8ur1W63A4dL9DabDZvN5k0vIsTExOB0Or0P75iYGNxud43ycLvdOJ3OKvM444wzeP3112nVqlW5PEpKShgxYgSLFy+mZcuWjB49mrfeeouOHTtWaIdSynsvBNpPBQUF5OTkVHg/BdpPZt9PBQUF5OXlVXk/efII5v00bel2DuYW8dJlQ8jPOUReDfyUkZFR4+eev58qQ0IxjayIfKWUGlbJb/FKqWLj/8eBVUqp9yrLa+DAgWr16tV1ssNzc3h4e8vbPPjDgwxrN4zHT36cWLsxkmPVbFj5JFy3ElICNxthIPHXEsmYpWXz5s306FF+vHdlfPDLHh79bCt7DxVyRGoid5x2VK1mo6xIh8vlQinlbQ9euHAhzZo145RTTgF057RSijPPPBO73c7Bgwdp0qQJAL/99ht9+vShuLiY+fPn06pV2f6x2uqrDdHry1w+27ifa+ev4abhXbmthrWE+uoQkTVKqYH+28Oxx+UzEbkIcACjgBfNOlBmZibNmh0e7nVR94sAmPfrPDKLMg93Sg/+l36pLTl8Z1f01xLJhIOWQKyF63Q6yw0RXbZsGffffz82m43169fTt2/fMr+73W7uu+8+3nrrLTIyMhARJkyYwNy5c4mPj0cpRXJycrmAYDbh4JNAEW5aMvOKmfzfDfRs3YQbTulS8/1M0hHSoCAipwI9lVLP+Gy+D1gOlAAvKKUCt/hoDbio+0WM7TyW5NhklFI4lVPXGJKbgtsF25dD1xHBNCmKCdz38UY27a28a+uXPw9R4io76qyw1MWdi9bz9o9/VrhPzyOacO9ZvSr8zcPpp5/O6aefDsAJJ5zAypUVT8D4yy+/sHz5crKzsykpKWHZsmWArml07dqVsWPHVnmcKJGBUoqpH/6Ko7CUN646jriY0L9PHJKg4Gk6Ukp9CXzp99tyoPLBuQGksjHknoAw84eZZBRmMOvkWcTYYmD1PFh6O0x4H7oMD4aJNSYY4+GDRTho8Q8I1W2viOqq9rt27eLEE0/0ft+9ezcfffQRe/fu5dFHH0VEyMjIICcnh8WLF3vTLV26lMLCQi644IIa21JfwsEngSKctHy8fh9LN+znztOPonurJrXa1ywd4dh8FDTS0ysf8iUidEzpSFJsEnbRnYkccyn88CIsvgWu/w7iw2e1tqq0RBrB0FJdiX7IQ1+yp4LF0NukJvLutcfX6BhVjSPfu3cv/fv3L/OwP/PMM2nRogW9evVi1KhR7NmzhwkTJvDTTz95m6E8fQ7BbhOPXl+B50BOEVM/+JWj26VyzUmdar2/WTrCJ2SGgOrG+V7S4xJuG3AbIsLu3N2U2u0w9ik49CcsnxkkK2tGOI+9ri3hoOWO044iMdZeZltt18L1jKapiBdffJFx48aV2ZaZmUmLFi2w2+1kZGRw8cUX06NHD8aOHUvbtm059dRTGTNmDMuXLw96aTccfBIowkGLUoq7399AUamLx8b3I8Zee3+apaNB1xRqOstgTkkOE5ZOoH/L/jw89GFiB14J3z8Pvc+FtuU670NCpMz8WBPCQYunM7m+o48q4rvvvuOTTz5h1apV3m05OTkUFRVhs9n48ccfueKKK3j55Zc54YQTAJgwYQLTp0+nS5ead0QGknDwSaAIBy0L1+zmyy0HmHpmTzo3r1uLg1k6GnRQqClN4ppwZZ8reeSnR2AFPHzqFGIzfw+1WVFMZtwxbQK6IDrAH3/8wZ133smHH37obRL6v//7P7799ltuuOEGQI9Df/PNN3nqqaeYNm0aoIejXn755SQkJFBSUsKTTz5J//79A2pblOCwO7uA+z/exHEd07nihA6hNqccDTooVPUChz+X9rwUpRSPrn4UQXjo0veItYXPjJS10RLuWEVLRX0K7du3Z/ny5WV+e+6558qkOeoo3UQ1b948cw2sBVbxCYRWi9utuOu99biVYtb5/bDZ6t43ZJaOBt2n4HlTsaZc1usybh94O5//8Tl3r7ib0iIHfHoPHNhskoU1p7ZawhmraHFXMpFiuE/IVhFW8QmEVsubP/zBqt8zmTymB+3Sk+qVl1k6Iu/qDCCFhYW1nn52Yq+JAMxaPQucxTy8bjExu3+Ef34GNns1e5tHXbSEK1bR4na7vdNgRDpW8QmETsuujHweXLqFk7o24+JBR9Y7P7N0NOiaQl2Z2GuirjHs+Zq7uw/Cufsn+PHlUJsVJUqUMMXlVty+cB0xduGR8/qG3TQbvjTooFCfKDux10QmDZjEZ4c280WnQfC/+/VQ1RBhlVIcWEeLVWoJYB2fQGi0zFu5k9V/ZDP9rF60TkkMSJ6WWWQnnKjvTXt578t57fTXOO2sOXrDJ3cHwKq6YaUHkJW0VIbvWguFhYWsWLGiwnThMnW2lXwSbC3b/s7l0c+3MrJnS87pH7jRbGbpaNBBwTOdb33o37I/ktaeradPZ0arNjjdlb+wZCaB0BIuhI2W9Qvgid4wPVV/rl9Qq92rWmTnrrvu4r333mPOnDnMnz+fiRMnMmfOHN58801vGrfbzciRI71TII8ZM4adO3fWTUs9CRufBIBganG63ExauI7kODsP/qNPQJuNzNLRoINCIFmdlMxXGb+QWZgJTuuM1GiwrF8AH98Ejr8ApT8/vqnWgaEiSkpKWLlyJUcffTRffvkl/fv3Z+HChRx99NHeoHDGGWcwduxYRIQLL7yQkSNHcuDAAW688UZGjhzJ/v0VrzUeJbx4/qvtrN/tYMa4PjRvHB9qc2pEgx59FB8fOCdd0uMSzm/RLMYAACAASURBVOp0Jk0+vhWlFO5z52AP4mikQGoJNUHT8sqY8tt6jYNBV8MX90Gp39xHpYXwyV3QdzzkZ8KCy8r+fsWSMl8rm4ripZdeYujQodjtdlasWMHevYdX9fM87MNt6uzo9VV7Nu51MPt/2zir3xGM6ds64PmbpaNBB4VAd9Q0iU9BNe3GzF9fIO+TK5h5xitBCwzRjsAAk7On4u2FWTXOoqKgsH//fmbPns0ll1xCVlYWEydOZObM8vNo7dq1K6ymzg4LnwSIYGgpdrqYtGAdaclx3D+26skX64pZOhp0UMjKygr4IhVy0m20/H0h72b8AivuZObQR4ISGMzQEiqCpsWvZF+GlLZG05H/9nb6M7lp1ftT8SI7K1as4PrrrycnJ4edO3fy7LPPsnDhQpKSkti/fz/NmjXjjjvu4PXXXw+rqbOj11fteOp/29iyP5e5EweSlhxnyjHM0tGgg4IpxMRx9RkvwaJ/8BSfI6vimDFkRlCbkqIEgOHTdB+CbxNSbKLeXg/Gjx/P6tWrWbx4MT/88AP9+/dn/PjxdO/enVdffZVx48aRn5/PsmXLwmrq7Cg155c/s3n+q+2cP6Atw3u0DLU5taZBBwXTph9uO4Cru09AbX+fp3csRhAeGPKAqYEhnBYOqS9hoaXveP35v/vBsVvXHIZPO7y9BlT14HY6nWzfvp3ffvuNxx9/3FtTWL16NVOmTPFOnd2rVy/Gjh3Lhg0b6NatG/Hx8UyaNIkRI4K7+l9Y+CRAmKmlqNTFpIXraNUkgaln9TTtOBBdZMcUTF1s49TJXHPSJNTvi3hm7TOICPefcL9pgSFcFg4JBGGjpe/4WgUBfyqb48jtdrNmzRouvPBCiouLGT16NN27d+fll1/mggsuYP369TzwwANhNXV22PgkAJip5dHPtrLjYD5vXHkcTRLMnTAzusiOCRw6dMi8zOOSIbkp1/a5in91GMtH2z9i2rfTcLkrH7teH0zVEmSsoqWyRXZKS0sZNGgQEyfqebQGDhxI+/btGTduHIsWLeLkk0/mzTffZM6cOYwYMYIRI0awYsUKLr/8ckaMGMHQoUP5+eefgynFMj4B87T8sCOTeat2cung9pzY1fz+F7N0NOiaQlUrYwWMbx7juq+eRw2/iee2v0ezxGbcOuDWgB8mKFqChFW0VLbIzpAhQxgyZAhAmQ7kzp07c95553nfVA2nqbOt4hMwR0t+sZPbF63jyPQk7j4jKEvMm+aTBh0UgsKgq+HHl7l+45c0PvEOTmk/PNQWRQljrDSdREPiwaWb2Z1dyIJrjyc5PrIfqw26+SgtLc38gySmwehHYd86JhzKpk2jNriVmw9//xC3qni+/boQFC1BwipaInHdhMqwik8g8FpW/HaQN3/4k6tO7MixHYLX92KWTxp0UCgsLKw+USDoeTZ0PxOWPwiZ2/n6r6+ZsmoKy/9aHrBDBE1LELCKlsoW2YlErOITCKwWR2Epd723ns7Nk5k06qiA5VsTzPJJgw4KRUVFwTmQCIyeBS17Q3Eupxx5CnNHzeXUdqcG7BBB0xIEwkXLkh1LGLVoFH1f68uoRaNYsqPql9X8sVJQCBefBIJAarn/400cyC3msfFHkxAb3KY/s3zSoINCUGnSGq76Ao44GoBBrQchImzN2sqsn2YFtCkpSv1ZsmMJ07+dzr78fSgU+/L3Mf3b6bUODP5Mnz6dHj16MGzYMIYNG8batWsDZHGUYLNs09+89/Nu/m9YZ45uZ501rK3T6FkHGjVqFNwDikBxHnz9MAz+P2jSmm/2fMNrm14jrzSPacdPwyZ1i9NB12IiwdJyxadXVPrb+oPrKXGXlNlW5CriPz/+hzGdxpBdlM1tX91W5vdXTn+lzPfKOo0nT57MhAkT6mh1aIheX2XJyi/h3+9voEfrJtx4atcAWFV7zPJJ0IOCiLQEFimlTqrk91jgfSAdmKuUMm1cXkimCsj7G358CbJ2wAVvcGXvKykoLeDlDS8jIkwdPLVOgcFK0x6Egxb/gODBUeyocHtd2bVrF5MnTyYuTs+P88orr1S4LdSEg08CRSC0TP3wVxyFJbz+z0HExYSmwcUsnwQ1KIhIGvAaUNX0fjcCa5RS00VkqYgsVErlmmFPbm5u8KcEbtoZhv0bvrgXNn2I9BrHjcfciEIxZ8McBGHK4Cm1Dgwh0WISwdLiX7L3ZdSiUezL31due+tkPQVyWkJalfuDntG0oqkIZs6cyZw5erW+uXPn8vHHH/P5558zePBgb5qKtoWS6PV1mI/X7WXJ+n3ccdpR9DyiSQAtqx1m+STYNQUXcAHwYRVphgGedS1XAAOBMsN0ROQa4BqAdu3akZGRAeipZGNiYrxLGMbFxdG4cWPvylU2m4309HQcDgelpaU4HA5SU1MpLi729uQnJydjt9u9qxrFx8eTnJxMVlZWmTwOHTrkfXkkLS2NwsJCb8dPo0aNEBFyc3UsS0hIICkpyZuHvcclpG18H/fiSWSn9EYlpHJDvxsoLilm/tb5FBUVMfX4qQhCXl6eN4/ExESys7MBPdwxNTWVrKws3G43DoeD9PR08vPzKS7Wi/w0adIEl8tFfn4+AImJicTHx3vfhIyNjSUlJcWbB0DTpk3Jzc2lpESXlFNSUnA6nd48kpKSiI2N9Z5jTx6ZmZneidqaNm3qPceePEpLSykoKKiRn3JycmjWrFmZPALhJ6UULpfLq9XTvONZIc1ms2Gz2XA6nfyr77+Y8eMMilyHO/MS7AncdMxNNc7D5XIhIsTExOB0Or3Hv+eee7j44otxu93s2rWLkSNHMmjQIK9Wl8vFqFGjGDBgAKWlpeXy8Pjf7XaXsUMp5b0XAu0nh8NR7f0UKD/V+n6y20lLSyM7O9vrh/T0dAoKCrx5NG7cGKUUeXl5OByOau8nTx7+99N+RwFT/ruBXq2SmTCwJU6nM2T3k2ef2j73PH6qFKVU0P+Ar6r47X9AivH/NcCFVeU1YMAAVVdyc3PrvG+92btOqelpSn14g3eT2+1Wj69+XPV+tbe6/9v7lcvtqnF2IdUSYMzSsmnTplqlX7x9sRq5cKTq82ofNXLhSLV4++Ja7e90Osttu/fee9X8+fO933fu3KkmTpxYJk1F22pCbfXVhuj1pe/PK1/9UXWbvFRt+zv056O+PgFWqwqeqeHY0ZwHJAIOoJHx3RSSkpLMyrp6WveFsU/Bkcd7N4kIt/S/BYXilV9fQUSYfNzkGrUdhlRLgAkXLWM6jWFMpwpWZ6shlc1i6dt8dMYZZ9Q5/2ASLj4JBHXV8t7Pe/hi8wGmjOlBlxah73g3yyfhGBTWACcCi4B+wPdmHSjkC4cc4zMCxeUEewwiwq399dxIyTHJNe5MCrmWAGIVLRUtsjN9+nSmT59e5X4dOnTg1VdfNc+wOmAVn0DdtOw9VMh9H21kUId0/jmko0mW1Q5LLrIjIqcCPZVSz/hsfg1YKiInAT2BH0JiXLBwu2DhREg5Ek5/EMAbGDwBYW/eXlont7bUCJAoUSIFpRR3vbcel1I8en5fbDZr34chGUullBpmfH7pFxBQSv0BjARWASOUUubMNU2YTD5ms0Nyc/jhedi9xrvZEwD25+/n/I/P54V1L1SZTVhoCRBmalGVzFxqBsEM4mbrasjX15s//Mk32zK4Z3QP2jcNn7WqzfJJWL7RrJTaq5RaoJQK7KBwP8Jmkq8R90GjVvDRDeAsOz6+ZVJLruh9BWO7VL1Qe9hoCQBmaUlISPCO6ggGwZoQTylFZmYmCQkJph2joV5ff2Tm8+DSzZzUtRmXHHekiVbVHrN8Eo59CkEjOzs7PC72hCZw5uPw9oWw6kk4+U7vTyLCVX2uAsCt3Hy26zNO73B6uVJo2GgJAGZpadu2Lbt37+bgwYMBz7si3G530JaxTEhIoG3btqbl3xCvL7dbccfC9dhFePjcvmHXfGuWTxp0UPCMaQ4LjjoDep0Da16FE27Ui8T7seyPZdy54k7WHljL3YPuLnORhpWWemKWltjYWDp2DF4nYUZGhmU6Zxvi9TVv1U5+3JXFrPP7cURq+fsx1JjlkwYdFMKO0bP0ZwUBAWBU+1Fc2vNS5m+aj4hw17F3hV3pJUoUK/D7gVwe+WwrI3q04Nz+bUJtTlBp0EEh7BYjT26qP11OOLARWvcr87OIcMfAO1BK8cbmNxCEO4+9ExEJPy31wCparKIDGpYWp8vNpAXrSIqz8+A5fcK24GWWT8KyozlYeF7nDzuWTYN5Z8ChP8v9JKIDwYQeE3hj8xs88tMjKKXCV0sdsIoWq+iAhqXlxRU7WLfbwYxxvWnR2LzO+/pilk8adFAI24VDBl+nPxffChWMlPEPDI+uftRSK2OFrV9qiVV0QMPRsmlvDk9+8Rtj+rbmzL5HBNGq2hNdZKchkXokDJ8Gv38B6xdUmMQTGC7pcQnzN83n+c3PB3UMfpQoVqPE6WbSwnWkJMbxwNm9Q21OyGjQfQqNGzcOtQmVM+hq+HURfHo3dBkOyeVHsXg6m5VSrNi9gpySHFLiU0JgbGAJa7/UAqvogIah5ekvt7F5Xw4vXzaQ9OS4IFtVe8zySYOuKYR1ydpmh7FPQ5MjIO9ApclEhLsH3c2rI14lJT4Ft3KHt64aEOn2e7CKDrC+lnV/HeK5r7Zzbv+2jOzZMgRW1R6zfNKgg4JnrYKwpUUPuG4ltOxZZTIRwV5qx+V2MWXlFJ5Y80RE38Rh75caYhUdYG0tRaUuJi1cR4vG8Uw7q+p7LZwwyycNOihEBJ51nf/3ABTlVJnUJjaSYpNIjq357KpRojR0Hvt8K78fyOPhc/uSkhhb/Q4Wp0H3KZg5V0xAydgK3zwGhdl6OowKSEhIKLf+wv78/bRMahlxASJi/FINVtEB1tXy484s5qzcySXHHcnQbs1DaFXtMcsnDbqmkJgYfq+uV0ibATD4elg9F/74tsIkHi2eALAnbw/nfnQuT/78ZMQ1JUWMX6rBKjrAmlryi53cvnAdbdMSuWd0jxBbVXvM8kmDDgqe9VkjglOn6KGqH90IpeXHJ/traZ3cmtM7nM68X+cx++fZERUYIsovVWAVHWBNLQ99soW/sguYdV4/kuMjr9HELJ806KAQUcQlw5lPQubv8M2sapPbxMbkwZM5v9v5zP11Lk/98lREBYYoUcxk5bYM5n//B/8c0pHjOjUNtTlhReSFxwASrPnuA0aX4TBqpp5R1Y+KtNjExpTBU1Ao5myYgyDceMyNYd/HEHF+qQSr6ABraSl0wp2L1tGpeTJ3nHZUqM2pM2b5xDqergOpqamhNqH2nHCD/lRK/xnz9VemxSY2pg6eilKKlze8DBD2gSEi/VIBVtEB1tLy1Dd72J9TxHvXn0BCbOSuKGeWTxp081FWVlaoTagbpYXwziXw3eGVTKvSYhMb046fxrldz+XlDS/zzNpnwropKWL94odVdIB1tPxv898sXLOb64d15pgjI3vRILN80qCDgtvtDrUJdSMmAVCw/EHI2gFUr8U3MLy0/iXWHlwbBEPrRsT6xQ+r6ABraMnOL+Hu9zfQtXkSNw3vGmpz6o1ZPmnQQSFiEYExj4E9Fj6+ucKZVCvCExheGPECx7Q4xmQjo0QJL6Z9tJHs/BKmn9GJ+JjIbTYymwYdFCJ64ZAmR8DI+2DnCvhlfo212MTGkDZDAFh3cB1zNswx08o6EdF+8cEqOiDytSxZv4+P1+3l5uFdOb57u1CbExCii+yYQH5+fqhNqB/9L4f2Q2DVbPJzq54CoyI+2fkJ7297n7yS8JrXJuL9YmAVHRDZWg7mFjPlgw30a5vC9cM6R7QWX8zS0aCDQnFxcahNqB82G/zjRbhyGcWlzlrvfuexd/LG6DdoFNcItwqfNuOI94uBVXRA5GpRSnHPfzeQX+LisfH9iLHbIlaLP2bpaNBBwRKktoOkdHA7IWNbrXa1iY30hHRcbhdTV03l+XXPm2RklCih4b+/7GHZpr+5Y9RRdGlhnTUhzKRBB4UmTZqE2oSAkbZyOrw6Rk+aV0eeW/scL6x7IWA21RWr+MUqOiAytexzFHLvRxs5tkMa/zyxo3d7JGqpCLN0VBkURMQmIslV/Da+NgcTkbki8p2ITKnk9xgR+VNEvjL++tQm/9ricrnMzD6olPb/J+RnwOcVntoqsdvs3H/C/YztPJZn1z7Li+teNMHCmmMVv1hFB0SeFqUUdy5aj9OlmHV+P+y2wy9rRpqWyjBLR3VvNHcAzhORnwD/Nz0EuBSoeBFh/8Qi5wB2pdTxIjJPRLoqpfzbO/oCbyul7qpJnvUlPz/fMrM/5jXqRMIJN8KqJ6HP+dBpWK329wQGpRTPrH0GEeGavteYYmt1WMUvVtEBkafl7R//4pttGTxwdi/aNy1bro00LZVhlo7qgoITcAFTgW+AlsBQ4GdgG1Cb12KHcTiAfA6caOThy2DgTBE5BdgAXKuUKteDKiLXANcAtGvXjoyMDACSk5OJiYnB4XAAEBcXR+PGjcnMzATAZrORnp6Ow+GgtLQUh8NBamoqxcXFFBYWevOw2+3k5OjRPPHx8SQnJ3vfHvTkcejQIZxObVpaWhqFhYUUFenZSxs1aoSIkJubC+h5z5OSkrx52O120tLSyM7O9kb79PR0CgoKvHk0btwYpZR3daWEhAQSExO9MyPGxMSQmppKVlYWbrcbh8NB+tA7YdOHqA9uJPuipTRp2hKXy+UdpZCYmEh8fDyHDh0CIDY2lpSUFG8eAPefcD+lpaU8/cvTFBQU8K8B/8LpdHrzSEpKIjY21nuOPXlkZmailEJEaNq0qfccA6SkpFBaWkpBQUGN/JSTk0OzZs3K5BGJfnI4HOX85MkjPz/f21HYpEmTWvupadOm5ObmUlJS4j3HZvrJ4XBUez+Fi592HypixpJNDO6QymldksnIyCjjJ4fDUe39FAl+8uxT2+eex0+VIZVNdyAiMcA8oDHQHZgIdAWuAv4LrALuVUqNrTT3svnNBZ5SSq0TkVFAf6XUQ35pjgV2K6X2icjrwCKl1EdV5Ttw4EC1evXqmphQjvz8fJKTK2wdizi8WnatgsW3wkVvQ9POdcrL5XYxZdUUFu9YzM39b+aqPlcF2NqqsYpfrKIDIkeL26246OXv2bg3h89uHUqb1PIl6UjRUh311SEia5RSA/23V1dT+AYYQdm+B+X3WVPyAI+HGlFxf8Z6pZRnnNVqdBAyjfj4eDOzDypeLR2GwP99B7a6v7Fpt9mZMWQGCsXsn2eTEp/C+d3OD5Cl1WMVv1hFB0SOlle/3cUPO7N45Ly+FQYEiBwt1WGWjko7mo1mm8+Bn4A9wNPAXUAf4HrguVoeaw26yQigH7CrgjTzRaSfiNiBccC6Wh6jVniqfVagjBabHYpzYcUscJbUKT+7zc7MITO5qs9VDGs7LDBG1hCr+MUqOiAytGw/mMfDn25hePcWnD+gbaXpIkFLTTBLR3VDUo8E1iqlTlVKHaeU6quUaq6U6gGcANRmlesPgEtF5HFgPLBRRGb4pbkfmA+sBb5TSn1Ri/yj+PLHd/DlA7Bqdp2zsNvs3Nz/ZponNcfpdrL8z+UBNDBKlMDhdLmZtGAdCbF2/nNOn7CeGj7cqbT5SETigXuAIhE5tYIkNnQNokYopXJEZBgwEnhEKbUfv5qAUupX9AikoBAbW5uYFt6U09JtFPQ6B1Y8Aj3HQvP6LSay8LeFPPjDg7w1+i36NDd1pLBl/GIVHRD+Wl76Zgdr/zrEUxcdQ4smVS9oH+5aaopZOirtaPYmEOkEPIh+WN8CZHp+AuKVUqtMsayG1Kej2fLkHYRnj4VmR8EVn3gX5KkLTreTlXtWMqzdsMDZFyVKANiyP4eznl7JyJ4tefbi/tFaQg2prKO52qeEUmqHUupCYBrwp1JqjfG3OtQBob5YZeEQqERLo+Zw2n/gr+9h9dx65R9ji/EGhPUH1/PGpjfqlV9VWMUvVtEB4aulxOnmtnfXkZIYywNn965RQAhXLbXFLB3VLscpIo2UUnlKqUU+2+KBKcArSqkdplgWBKywcIiHSrX0uxAyt0HniloA68b7297nvW3v4VIuJvaaGLB8PVjFL1bRAeGr5Znlv7NpXw4vXjqApo1qNhonXLXUFrN01GSN5qkikqSUutFnWwJwCHgCONsUy6IEBhEYPk3/72kqrGf1esrgKeSV5jFr9SwAUwJDlCjVsX73IZ5d/jvnHNOG03q1CrU5lqEmzUd3ARki8pLPNodS6jHKT30RUTRt2jTUJgSMarUUOeCdi2HDoqrT1YAYWwwPnfQQo9qPYtbqWby+8fV65+mLVfxiFR0QflqKSl3ctmAdzRvFc+9ZvWq1b7hpqStm6ahuQryOInIk8CpgF5EZInKk8TcAiOh6mOe1eStQrZa4RpB3AD65U0+cV09ibDE8NPQhRrYfyaOrHw1oYLCKX6yiA8JPyxPLfuP3A3k8fF5fUpJqNwon3LTUFbN0VNd89DB67iOFHm00Ct1ctMHY9qgpVgUJz3wkVqBaLTY7nP0MvHASfHo3nFv/ZThjbbE8PPRhWAGPrn4UEeHSnpfWO1+r+MUqOiC8tKzelcVL3+zgokFHcnK35rXeP5y01AezdFQZFJRSZabGFpEmwBfATUqp+hc3owSXFj3gpEnw9UN6JtVup9U7S9/A8MhPjyAIE3pOCICxUaKUp6DEye0L19EmNZHJY3qE2hxLUl3z0XQROcLzXSmVA8wAOpltWDBISUkJtQkBo8ZaTroNmneH5Q8e7niuJ57AMLL9yIDkZxW/WEUHhI+Whz/Zwq7MAmad349G8TUZJ1OecNFSX8zSUdUbzQJsBRYYgWEPUIhuRkJEbECSUup4UywLAk6n0zJvN9ZYS0w8jH8dkpvXexSSL7G2WB47+THvOPGMwgyaJTarU15W8YtVdEB4aFn1ewavffcHVwzpwOBOde9kDQctgcAsHVVNiKeUUm8rpU5Ev5MQD9yqlBpp/A2P5IAAeOc0twK10tL8KL2us8sJh/4KmA2egPBb9m+MeX8MH22vctbzSrGKX6yiA0KvJbeolDsXradTs2TuPK17vfIKtZZAYZaOGs17oJR6C72eQqEpVkQJDYuugPn/gNKigGbbsUlHzul6Dse3jugyQ5QwYsbizexzFDJrfD8S4+o+LXyU6qk2KHjWSVZKbfZ9e1lErjfTsGCQlJQUahMCRp20DLhcv+28IrCDyGLtsdw16C7v7Kqr9tRuNhSr+MUqOiC0Wr7c8jfvrv6La0/uTP8j6/9qlFX8YpaOmtQUngEQkWXG5xJj+2WmWBRErNCu6KFOWroMh34X6XWd9/8aeKOAtza/xXVfXMc7W96p8T5W8YtVdEDotBwqKOHu9zZwVMvG3DIiMGtuWcUvZumobvTR2UCh8QJbrN9n3afcDBM8a5pagTprOe1BSEiFj27QfQwB5qLuFzGs3TBm/jCTd7e8W6N9rOIXq+iA0Gm596ONZOWX8Nj4fsTHBKbZyCp+MUtHpQ92ERmNXiktFv0SW1fjs7vx2cYUi6IEl6R0GP0IlBRA3v6AZx9rj+Xxkx9nWNthzPhhBgu2Lgj4MaJYk0827OPDtXu58dSu9G5jjWGkkUBVpf2vgP8AxUqpi4B1xudq4zNiZ0f1YJVqJNRTS69z4LqVkFL5Eob1IdYey2PDHuPktifzwPcPVBsYrOIXq+iA4GvJyCtm8ge/0qdNCv93SueA5m0Vv4Si+agv8C1wrIjMA/oYnwOMz27GZ8RilZdYoJ5aRCAmTq/r/P0LAXupzZc4exyPD3u8RoHBKn6xig4IrhalFPe8v4G8IiePje9HrD2wLdVW8YtZOqp6T+F7oAdwNTAQ+AF4CD3/0cPAMOAxU6wKEpmZmdUnihAComXTh/DpXfCLOQvoeALD0LZDeeD7B1j428IK01nFL1bRAcHV8sHaPXy+6W8mjepGt5aNA56/Vfxilo4qQ7DSa3XGADegA8AxQDul1Fal1Bal1EZTrAoS1S1FGkkEREu/i6H9EPhsMuQGvn8BdGB4YtgTDG07lLe3vE2pq7RcGqv4xSo6IHha9juKuPfDjQxon8ZVJ5kzm45V/GKWjupGH10NePoRvgPWASNFZI2I3GaKRUHESmu5BkSLzQZnPQXOIlh6e/3zqwRPYJg7ai6x9thyF7dV/GIVHRAcLUop7npvPSUuN7PO74fdZs4xreIXs3RU11i3CjhfKVUgIhOM2sFd6EnxtptiURCxymIbEEAtzbrAsLth88ewqW7TVNSEOHscaQlplLpKue2r23h/2/ve36ziF6vogOBoeeenv/j6t4P8+4wedGyWbNpxrOKXkCyyAzwLeF6b+6eI2ETkDXRzUsQ3zFllvDIEWMsJN8KxV0Gr3oHLsxLcuClyFVHoLGTJjiWMWjSKvq/1ZdSiUSzZsaT6DMKY6PVVc/7KKmDG4k2c0Lkplw5ub+qxrOIXs3RUO/esUirP+NeNXpv5FeA79CI7EU1pafn27EgloFrssTAmOGMI4u3xPDv8WT7Z+QnTv51OkUvPw7Qvfx/Tv50OwJhOY4JiS6CJXl81w+1W3LFoHSLCI+f1xWZSs5EHq/jFLB3V1RR8H/wdgDeAfxmfi0Qk+iaSlcnPhLcuhB1fmXoYm9iY/fNsb0DwUOQqYvbPs009dpTQ8/p3u/h+RxZTz+xB2zRrzEsUyVQXFHxD9g6l1DnAMuAapdQYIK/i3SIDq4xXBpO0xCVBxlb4+Gb9xrOJ7M+veLRTZdsjgej1VT07Dubx0KdbOOWo5owf2M6UY/hjFb8E/T0Fg1UikiAiMUAjY1sMeuGdZ5VS/6zNwURkroh8JyJT6pMmUFilGgkmaYlN1KORsnfBVw8GPn8fWiW3qnB7i6QWph7XTKLXV9W43IrbF64jPsbOQ+f2DdqoIKv4JSTNR0qpTM/IBQAAIABJREFUKUBj4F3gOhFZDIhS6lTgudocSETOAezGwjydRKTclIc1SRNICgrMLf0GE9O0dDxJT7H93bOwZ405xwBu7n8zCfaEctsLSwvZlLnJtOOaSfT6qpqXv9nBz38e4v6ze9GySXnfm4VV/GKWjio7mo1pshV6youZwFFAiYgMA2wiEqeUGl3DYw0DPH0Qn6Mn29tWhzSIyDXANQDt2rUjIyMDgOTkZGJiYry98nFxcTRu3Nj75p/NZiM9PR2Hw0FpaSkOh4PU1FSKi4spLCz05mG328nJyQEgPj6e5ORksrKyyuRx6NAhnE49q2haWhqFhYUUFek28UaNGiEi5ObmApCQkEBSUpI3D7vdTlpaGtnZ2bhcLgDS09MpKCjw5tG4cWOUUuTl5XnzSExMJDs7G4CYmBhSU1PJysrC7XbjcDhIT08nPz+f4uJiAJo0aYLL5fKu0JSYmEh8fDyHDh0C9NwpKSkp3jxAD3PLzc2lpKQE0FVU50n3ELflE1yfTsN50UJiY2O959iTR2ZmJkopRISmTZt6z7Enj9LSUu9FXJGfRnccTW5uLnO2zuFA4QFaJbfirCPP4oOdH3DZ0st44IQHGNpqaET5yeFwlPOTJw9T/OR0evNISkoKqJ8cDke19xNQ4/vpx627eezzrQzvls7YfkcE1U8Oh6Pa+ykS/OTZp7bPPY+fKkOqeitORBKAFGAh8BowDnAA/wb2AbFKqRqtxiYic4GnlFLrRGQU0F8p9VBt0/gzcOBAtXr16pqYUI7CwkISExPrtG+4YbqWPT9DWgc9q6rJ+GrJKMzgluW3sO7gOm465iau7nu16ccPFNHrq2JKXW7GPbuK/Y4iPr91KE0bxQck35piFb/UV4eIrFFKDfTfXl3zURG6M/klpdRcpdRZ6EV3LlFKOWsaEAzyAI+CRpUcuyZpAkZMTLUjciMG07W06X94Xee8g6YeyldLs8RmzDttHmd3PrvSfodwJXp9Vcyzy39n494cZv6jd9ADAljHL2bpqPahq5TKV0q94fP9++pK75WwBt0cBNAP2FXHNAHDKi+xQJC0KAVvngsLLgWjemwG/lri7HHMOHEGZ3U+C4Cv/voqIkYlRa+v8mzY7eCZL39n3NFHcHrv1gHJs7ZYxS9BX2THBD4ALhWRx4HxwEYRmVFNmsh+pdVqiECf8fDnd7B6bkhMKCgt4N5v72XW6lkhOX6UulPsdDFp4VqaNorjvrHmvy0fpW4ErR6llMoxOqhHAo8opfajJ9irKo2pIT0uLs7M7INK0LQcfTFsWAhfTIejzjBlYZ6qtCTFJvHKaa+QnqD7NkpcJcTZw9OP0eurLE8s28Zvf+fxyhXHkpIUuoVurOIXs3QEdZ1lpVS2UmqBERDqnCZQNG4c+LnaQ0XQtIjAWU+CcsPi20xZkKc6LZ1SO5GakEqpq5SrP7+aWT/NwuV2BdyO+hK9vg6z5o8sXlqxnQuPbccpR4X23ROr+MUsHUENCuGGVRbbgCBrSesAp07RL7UVZAU8+xprEeiW1o3XNr3GjV/eSG5JbsBtqQ/R60tTWOLi9oXraZ2SyOQxPQJoVd2wil9CsshOlCiVctx1cN03kBy6aYhjbbFMHjyZqYOn8t3e75iwdAJ/5vwZMnuiVMzDn25hZ0Y+j57fl8YJ1lgf2co06KBgs1lHftC12OwQEw9FObD2rcBmXUst448az4sjXySzKJOLl17MD/t+CKg9dSV6fcG32zN49dtdXH5CB07o3CzAVtUNq/jFLB3WODt1JD3d/BexgkXItKyeBx9cD9u+CFiWddEyqPUg3h79Ns0SmnHtsmt5Z8s7AbOnrjT06yu3qJQ7Fq6nY7Nk7jq9uwlW1Q2r+MUsHQ06KFhlvDKEUMvg66HZUbD4FigOTJt+XbW0a9KON0a/wYltTmTmDzOZ8f0MSt2hm/ysoV9fDy7dzD5HIbPO70tinN0Eq+qGVfxihfcUwg6rzJYIIdQSEw9nPwOO3fC/+wOSZX20NIprxOxTZnNF7yvYl78PWwgv8YZ8fS3feoC3f/yLq4d2YkD78CqZW8UvZumwxvveUUJLu0Ew6Br48SXofR4ceVxIzbHb7Nw24Dacbid2m52/8/8mrzSPzqmdQ2pXQ8FRUMrd762nW8tG3DqiW6jNiVJLGnRQqGqmwEgj5FqGT4MiBzSq/xj0QGmJsenL+4HvH2Bz5maWnruUeHvw5toJuU8CSG20TP94I5l5Jcy57FgSYsOn2ciDVfxilo4GHRSKi4stMzlWyLXEN4JzXgxIVoHWMmXwFP7I+cMbEDxTEptNyH0SQGqq5dNf9/PfX/Zw8/Cu9GkbniucWcUvZulo0H0KnjnfrUDYaMn9G965BP7eWOcsAq2lVXIrjmutm7Te2fIOU1ZNodhVHNBjVETY+CQA1ERLZl4xk/+7gV5HNOGGU7sEwaq6YRW/mKWjQQeFKCZgj4X/b++8w6Sqzj/+OdN2tnelLdJREBcVA4hKMSBmLQjRhKixJVgQiS2KMSCIifkpRsTeYoyxEBKwoAIqqImigFIkBJEiRdq22T71/P64M7OF2d3Z3Sn3zp7P88xzZ+4599zznXfmvOeeunctvDUDdLj0RIWrgrd2vsV1K66juLY43tlJGKSU/G7pN1TWeXjksqFYzapoMSqd2nKpqanxzkLE0I2WlBw4/0/a1p1fPN2uJKKpZdop01gwegHbS7czdflUtpVsi9q9dGOTCNCalrc2/cD7Ww9x6/gBDOyi77WFEsUu0dLRqZ2C2ay/TrD2oistJ0+BARPho/lQurvNl0dby4ReE3j5/JcBuOr9q1i5Z2VU7qMrm3SQlrQcrqhj9ptbObVnFtPO6RPDXLWPRLFLtHR0aqcQ2Dc2EdCVFiGg6BEQZvjo/jZfHgstJ+WexGtFrzEgewC3f3w7T218Cp+M7MZBurJJB2lOi5SSu/+5GafHy4JLCzGbot+B31ESxS7R0tGpnYIiimR2h6mvQtGCeOekWQJbfV7U9yKe3PQkd3x8BzXumnhny1AsXr+P1duPctfEE+mTnxbv7CgigPHHZXWApKTY7w8bLXSppfc52tHrBncN2MMbohhLLTazjfmj5jMgewDPb3me4tpielp7RiRtXdqknYTSsr+shvvf2caIPjlcNbJX7DPVThLFLtHS0amfFBKlwwl0rMXng5eKtNFIYRJrLUIIrhp8FcsnL6dnRk+klOxx7Olwurq1STtoqsXnk/x2yWaklDz000JMBmg2CpAodlEdzVGgtDTyG8TEC91qMZmg/wT475uw7e2wLomXlgxbBgBvbH+DyW9NZnvp9g6lp1ubtIOmWv629ns+21nCvRcMoiAnJU65ah+JYpdo6ejUzUeKGDFqJmxdBsvvgF5nQ7K+lxmY2GsiVe4qBmSrdXtCsbu4mgff+x+jB+Tz8zMK4p0dRYTp1E8KibLZBuhci9kKFy+C6iOw6vetRo+3lix7Fr8a8iuEEOyr3MesT2dR5apqczrx1hFJAlq8Pskd/9iE1Sz405RTYrJcSKQxul2W71rOhCUTGLd8HBOWTGD5ruURTd/Y304HSZTNNsAAWrqdCiNvhv3rwVXdYlQ9adlavJX3dr/H5e9ezr6KfW26Vk86OkpAy/Of7mLD92XMvXgwXTLtcc5V+zCyXZbvWs59n93HweqDSCQHqw9y32f3RdQxdGqnUF5eHu8sRAxDaBn7O5i2Bmwtd5DpScvE3hN5dvyzlNSVMPXdqXx58Muwr9WTjo5SXl7Ot4crWbDyW84bfDyThnaPd5bajZHtsvCrhdR56xqdq/PWsfCrhRG7R6d2Ch6PJ95ZiBiG0GK11+/rvO2dZqPpTUtgq89cey7Xr7qeN/73RljX6U1HR6hzurh98SbS7BYeuGSIIZuNAhjVLsW1xRysPhgy7FD1oYjdp1M7BUWc+OT/YPGV8MPX8c5J2BRkFPD3n/ydM7ufyfwv5sd9q89YsezrA4x68CNG/HkdWw44uKiwK3lpiTHO3yiU1pWyYP0Czv/n+c3G6ZLaJWL369ROITs7O95ZiBiG0nL2HZB6HLw5Q5vY1gS9akmzpfHY2Me4ZvA1vLH9DW5cdSMOZ/P75OpVR7gs+/oAs/61mQPl9Us0v7FuP8u+PhDHXHUcI9ll6Y6lTPznRF7+78uMP2E8tw+7Hbu5cV+O3Wxn5mkzI3bPmA1JFUK8AAwClksp5zcTxwLs8r8AZkgpt0QrT7W1taSlJcbUfENpSc6CoofhjSvgs8fg7NsbBetZi9lk5rZht9Evux/3fXYfK79fyaUDLg0ZV486XB4fpdWu4Kuk2tngvYvSKhelNdrnXUer8MnG19e6vTy0YjuTTjVun4Ie7dKQClcFPp+PLHsWBekFjOkxhhsKb6BPlrbYYH5yPgu/Wsih6kN0Se3CzNNmUtSnKGL3j4lTEEJMBsxSypFCiBeFEP2llDtCRD0FeE1KeVcs8lVXV6frH0dbMJyWky6EQRfDmj/BSRdBXv9gkBG0XNT3IgrzC+mZri2J4XA6yExqvIxHLHTUuDyUVLkaF+zVTkqr3f5j4JxW4Fc6Q7enCwHZKTZyUrVX/+PS+O5I6GG4P5Qbe5MaPf++atw1XLj0Qs7rdR73DL+HYV2GMazLsEZxivoUUdSniOLiYvLy8iKeh1g9KYwBFvvfrwTOAkI5hRHABUKIscAW4Hop5TG/YiHENGAaQEFBAcXF2mYpqampWCwWHA7tkd5ms5Genk5JSQmgjU/OycnB4XDgdrtxOBxkZWXhdDqDuxilpqZiNpuDKxAmJSWRmpoanD0YSKO8vDzYYZWdnU1tbS11ddqogLS0NIQQVFZWAmC320lJSQmmYTabyc7OpqysDK9X24gmJyeHmpqaYBrp6elIKamqqgqmkZycTFlZGQAWi4WsrCxKS0vx+Xw4HA5ycnKorq7G6dR2FcvIyMDr9VJdrQ0BTU5OJikpKTj6wmq1kpmZGUwDIDc3l8rKSlwuFwCZmZl4PJ5gGikpKVit1uB3HEijpKQkuM1lbm5u8DsOpOF2u6mpqWlkp4rhs0hzOnHVukiTMminiooK8vLyGqWhRzulkorL5WK3YzfXfnAtNw+6mYv6XRS0k8PhOMZOgTRC2amqqopKp5dan5kqN+w7UkZ5rYcKp49qr4mDpZWU1bgpq3VTUafV+Os8oVd2tZgEuak2Mu1mspItnHRcCl0GHoddeMhKtpCTYuWELrlYpYt0K2TYLeRkZzWy06Z9ZfzgOHaHuuMzbBQXFx/zf9KrnaDx/8nhcLT6f2rJTpH+P3mEhxU7VjC221isVis3Fd5ET1tPiouLW/w/Bf6DbS33AnZqDiGlbDawvQghngEGNjg1GhgqpdwkhJgAnCalfDDEdWcA+6WUB4UQLwNLpJRvtXSvYcOGyfXr17crn3V1ddjtxhxr3RSlJX7UuGt4aP1DTBsyja5pXYPnq6prqPWZKatxNajNO4M195JqF2VN3nuattf4SbGZyU6xkZtWX5vPTbWRk5rkP9rIDpxLs5GeZOnwCCGtT2ELte76HfSSrWb+OHmIoZuP9PL7qvPUsXj7Yl745gVK60pZdvEy+mb1bf3CzYvhw3lIx35EZg84dzacclmb7y+E2CClHNb0fFSeFKSU1ze5+UIg2f8xjeY7uDdLKQNVk/VA/2biRQQjD6triqG1VPwAK+6BCfMhs4dutTg9Xq0AD9FcU1c9mfu+O0BJ9U72yWXUlYygojqZ5upcGXYLuWlJ5KTaKMhJYWhBVrCwry/0k8hJ0wp6uzX2G8MECv6HVmznh/JaumUlc+d5Aw3tECD+/xWX18WSb5fw/JbnOVp7lBFdRzB96PTwHcLbt4C7FgHg2Kd9hnY5hlDEqvloA1qT0VqgEGhupbG/CSEeAL4BJgF/iGamKisrE2YZXUNr8Tjh2xVQshNqy7A59kMHakDhIKWk2uWltKpxZ2vjwr5BG32Vi2pX6D2nTYJgQZ6SdoQ622qSUtczJfU3DOk6tL5W76/lZ6fYDLOH8STzf5iUNA9p349I6gHm2UB0bBIrwv6vOKvA62rwcoPFru0VArDvS3DXNo6TWQA9/JXvL55tdK3bU8tSm+TZw//hcM1hTjdn8qfkQZzhcMNHD2nxBk+GoVOhugRemazd0+usv7+7Vns1xF0LH84znFNYBnwqhOgGnA+MEEIMAn4hpby3Qbx5wKuAAN6SUn4Qo/wp4klObxhYBN/8AyBYA/K8OUP7gYbxY/f5JI5ad3DkTKjmmqaFvquZ9nibxRRskslJtdE7N6W+aSZVq90HmnFyU21k2K2Nlo7eVnIyt6y+hY9rH2BCtweY0GtCx7+jeBDJWqmU4PNohVtgRntNKdSV+ws+f+EpgR6na+H7N0DF/sbhFjsU/lwL3/Q6lHxXX2B6XdpQ5zH+cSqr5sDR/zUOzx8IZ87Rwv92CRzd3iB9N/Q+G37hn5z4xHDt/g0ZdDFcpm3lyt8v1fLfkKGX1zuFFbM0zcDy1BQWZWdxwGqhML+Q+SPnMHzx9QhTBZht/pcV3P4lYMwWSDteO9cw/OtXQn+/jv2hz7eDmDgFKWWFEGIMMB74PymlA3AA9zaJ9w3aCKSYoId2xUhhdC01O/9N0wWYLd46nG/+hvLNq6hz+3B6fDg9XvZY+vJ+yoWUVDu5tPgpTO4qXB5fcPjkRtmPN7xjAZhn+QtdzF6SLGaSrCaSLCYO5J3O94UXkJNiYfzOP2K3mrRwi4kkqxnLgB8jBp8Prhp431/ASKDK/xpYBL0mQm0ZrJp1jJaTBk/mtaLXuGXlDdz+8e3c9EUvbrCfUN9sUTgVTjgTyvbApyF2pjv9auh+ulZgff74seHDb4DjB8PBTbDu+WPDR/0GcvvCvnXw9cvHhp/zW8gqgN2fwpbFx4aPmw1p+fD+rNC10g/u05zChr/CxlfrC1Sfv3C9aa02c33VbFj3Qn2BDmCywmxtYAgr74WNf2+cvj0L7v5ee/+fR2Fbky7FjB71TmHzYtj5kXYvsw1MFjhuUL1TqDoMlQfrC1VrMtjS6v8rXYdCejewNCh08xqsjDv6t+Cp086b/IVzVoMNmH7+qjZsK3Ct2QbJ9XMgvLdtw2ROQliS2Ln5abIOruXeU29mVLdR2m/htv8e+90Hv4dMuDyEbXat0ZxzUzJ7NJ9WG4nZPAUpZRn1I5B0QUqKsdaBb4lYaPH6JHVuL06Pr8Vj4L0zZJhWsDc9vlpz0P+I0Bibpxq5YxVJQOCBf6eoYFv6aHJTbfyILWSYKzBZBCYTmITgnJ49uHL0WeSm2Tj+L/dg8jYZQdNrIIw/CXxe2PDZsTfNOUE7+tywY9Wx4fknaUd3Xejw7qeT13csLw6fx/1vXsqT7OE7xy7mV3q1jrVe/h3p6hyhrx/gn7laUxo6/OQp2rHqaOjw067SjpU/hA4fcZN2dOwPHX727UA+1BQfGwZaHxCAMGkFalJa44Ix0JHS4wztOw7Wdv3HAKdeqe3O17A2bGlQuRk/D0bf5S/0A3EaNPtcvkTbr6M5Lnk65OkU/8ggfjyn+WsBTr+q5fBeo5oN2le5j5s+uIk7ht3B6ILR3Dh0OjNOm9nx/oxzZwef3oJYk7XzESIqo49iSXtGHy37+oChO898Pkmdx4vT7QseDx0tITktQyt4/QVy0+MxhXiD6xseAwW1s0nB7fa2/7diEmC3arXxRkf/+0cOXEEP07GF0H5fHvuu+jLYXJOVbMVikPb44uJicnNzefm/L7Ng/QJOzDmRx8Y9FtElCaLKn09uplZaALd+E/v8RIhoje/3SR8/VP1Aj/QeuH1ublt9G5cPupwRXUdE9kZGHH2kZ5oOsztQXsusf2mTptvqGHw+GWzSaFjzbW8tuuXadKCA71jhLATY/U0pdos52HQSOKYlWchN1T6HLMSbHINNL03SaXi0W81YTKLFWtJ986/gt+4nSRGu4LkaaeN52xXc1ze33XrjTWCrz96Zvbnrk7v44xd/ZOG4yK1oGVViUCtNBKSUrNm3hic3PUlxbTHvTn6XZEsyi85dFJ0bnnIZnHIZJQafvKYbHlqxvdG4a9Cm7v9u2Ra+2F0SRqFeX4t2eUN3VIZLSwVvapKFnNT6wrvp0e5vH9dq2yY8zjpys9KDcbQC2dwojt1ixmpuuXCOF0OLpjF7qYffyNfpJkr4QebyKD/nrKJp8c5auzGb64eRntPjHF75ySvBWc9unxuryRqvrIVHoPYZgVqpnmhol44gpeTfB/7NExufYGvJVgrSC7jt9NuwmWytXxwBIqWjKZ2u+aj33ctpTvFx6UmNar9Nj0lNar+t1Z5but5mNumycI4nRm/WCxePz8P0D6czOHcwt5x2S7yzo2gjUkrWHlzLExufYNPRTXRP6871p1zPhX0vxGIyTj1bNR/56ZaV3GjVxwDds5L5z93j4pCjyFBWVmao1R9DMenU7kw6tXtCaIHmbSKRFKQX0CM9ciNGok2i2AQ6pmXdoXU8sfEJNhzeQJfULsweOZtJfSdhNcf+qS9aNul0TuHO8waGnLp/53kDW7hK/wTWfEkEEkVLczqsJiv3jqgfjf3J/k/ondmbgvSCWGWtzSSKTaD9WqSUPLz+YY7WHOWe4fcwpf8UbObYNBWFIlo26XROIVGn7iuMidPrZN7n83B6nTwy5hHO6HJGvLOkaMAuxy4WfbWI2SNnk23P5uHRD5OfnI/dYux5QS3R6foUGuLz+TC1NM7ZQCgt+iNcHXsr9jLjoxnsrdjLrOGzuGyg/jpyE8UmEJ4Wj8+DxWThu7LvuG7ldTw8+mHdOeyO2qS5PoXEsHI7CSwRnAgoLfojXB09M3ryyk9eYUS3Edy/9n4eWPuA7rb6TBSbQMtadpTt4NbVtzLrU22mer/sfqz66SrdOQSInk06tVMIrLWeCCgt+qMtOtJt6Tw+7nGuHnw1r29/nRs/aHmrz1iTKDaB0Fp2OXZx58d3MuWtKaw9uJY+mX0ItKLEs9+gJaJlk07Xp6BQ6BWzycztw26nX1Y/5n4+l18s/wWLxi0KbsOoiDx7K/by1KaneHf3uySZk/jVkF9x1eCrjtlFrzPRqfsUnE6ncZebboLSoj86omPjkY3MXD0TgeC9Ke+RbElu/aIokig2AU3LUddRntn8DG/vfBurycrUE6dy9clXk2PPiXf2wqajNlHzFEJgdIfYEKVFf3REx9DjhvJ60evsKN8Rd4cAiWMTgCpXFVPemoLH52HqiVO5bsh15CVHfrmIaBMtm3Rqp1BVVWX4JacDKC36o6M6uqZ1DW7vuey7Zaw7tI45I+fEpY3b6DY5UnOElXtWcsWgK5BOyf2j7qcwv5DjU4+Pd9baTbRs0qk7mhUKo3Ck5ghHao5gEuov2x5W7FnBgvUL+L5C26thQq8JhnYI0aRT9ylUVVWRlpYW4RzFB6VFf0RaR2DsfHFtMSW1JQzMid0sfKPZpKyujL9s/QsDsgdwQZ8LcHqdHKk5QkF6geG0NEdHdah5CiFITo5/W22kUFr0R6R1BBZbe/DLB7nyvSv54PvY7VZrFJs4nA4e++oxJv5zIi998xI7ynYAkGROCi4jYhQtrREtHZ3aKZSVlcU7CxFDadEf0dJx94/upn92f25dcytPb3o6Jp3AerdJpauSpzY+xcR/TuS5Lc9xdo+zWXbxMm49/dZj4updS7hES0en7mhWKIxIXnIeL573InM/m8sTG5/gu/LvuH/U/boYpRRrqt3VvLrtVV7a+hIVrgrO7XkuNw29iQHZA1q/WBGSTu0ULJbEka+06I9o6kgyJ/HAWQ/QP7s/f97wZ/ZW7I3qVp96tMkuxy6ufu9qypxljOkxhhuH3sig3EGtXqdHLe0hWjo6dUezQpEIfLzvY+769C6SLck8OvZRCvML452lqFHnqWNn+U4G5w3G6/My/4v5TO43mSH5Q+KdNcOhOppDUFpaGu8sRAylRX/ESsfogtG8cv4r2M12rn3/WraWbI34PfRik7mfz+WGD26gxl2D2WRmzsg5bXYIetHSUaKlo1M7BZ+vY3ss6wmlRX/EUke/7H68VvQa1w65lhOzT4x4+vGyidvnZsm3SzhQdQCAa06+hkfGPEKKNaXdaarfV8t0aqegUCQSWfYspg+djtlk5lD1IX7/n99T5aqKd7bahcfnYemOpVy49ELmfj6Xd3a+A8CA7AG6XMY6kUiMHpd2kpNjnMWvWkNp0R/x1LHp6CZW71vNNYOvIc3W8YlasdLi9Xl5d/e7PL3pafZW7mVQ7iDuGX4PZ3c/O2L3UL+vlomZUxBCHA8skVI2a10hhBX4F5ADvCClfDGaeaquriY9PT2at4gZSov+iKeO83qdx5ndziTdlo6Ukj0Ve+id2bvd6UVbi0/6WLlnJU9uepLdjt0MzB7IwrELGVswFiFERO+lfl8tE5PmIyFENvBXILWVqDOADVLKUcBPhRBRtZzT6Yxm8jFFadEf8daRbtP+Pm/ufJPJb07mH9/+o91pRVPLlqNbmPLWFO785E7MwswjYx5h8YWLGddzXMQdAsTfLpEiWjpi9aTgBX4GvNlKvDHA3f73nwDDgNVNIwkhpgHTAAoKCiguLgYgNTUVi8WCw6HtWGWz2UhPT6ekpAQAk8lETk4ODocDt9uNw+EgKysLp9NJbW1tMA2z2UxFRQUASUlJpKamBnv6A2mUl5fj8XgAyM7Opra2NrgTUlpaGkIIKisrAbDb7aSkpATTMJvNZGdnU1ZWhtfrBbRHwZqammAa6elaDa+qqiqYRnJycnAWo8ViISsri9LSUnw+Hw6Hg5ycHKqrq4M/loyMDLxeL9XV1YA2LT4pKYny8nIArFYrmZmZwTQAcnNzqaysxOVyAZCZmYnH4wmmkZKSgtVqDX7HgTRKSkqQUiKEIDc3N/gdB9Jwu93B7QNbs1NFRQV5eXmN0jCq7WRdAAAKzElEQVSinRwOxzF2CqQRSzsNTR3KsOOGMe/zeWw5uIXpJ03HYra0yU4Oh6PV/1Nb7FRSUkKNp4b0pHQykzLxer3cO/RexnQbQ15OHjXVNVGzk8PhaPX/FA87tfX/FLimreVewE7NEZV5CkKIZ4CGq3V9JKWcJ4RYI6Uc08J1HwKTpZQOf8FfIaV8vaV7dWSegsvlwmbT51Z7bUVp0R960uH1eXn0q0d5aetLDO86nAWjF7Rpd7FIapFScuMHN2I1W1k0blHwXDSeCkKhJ7t0hI7qiOkmO1LK69t5aRWQDDiANP/nqBGoVSQCSov+0JOOwFaffbP6Mu/zedpWn+cuok9meFt9RkLL10e+pjC/EJMwMa7nOKwma9AZxMohgL7s0hGipUNvQ1I3AGf53xcCe6J5s8AjXCKgtOgPPeqY1G8SL573IlXuKi5ffjmf7v80rOs6omXD4Q1cu+JafvneL/lw74cAXDbwMi7pf0lMnUEAPdqlPURLR9ycghBinBDi5ian/wrMFUIsBAYBX8Q+ZwpFYhPY6rN7Wndu/uhm3vyuta6+9rHxyEZ+vfLXXP3+1ex27ObuH93NOT3Oicq9FJEjpvMUGvYnSCk/Aj5qEv69EGI82tPCbCllVJ/zEmVddVBa9IiedXRN68rL57/Mg18+yKnHndpq/LZo2Vq8lcc3Ps6/D/ybHHsOdwy7g58N/Bl2iz6289SzXdpCtHR06gXxPB5PwqyYqLToDyPpkFLy3JbnmNx/cshN7MPRsr10O49vfJw1+9aQmZTJNYOvYeqJUzu0JEU0MJJdWqKjOtSCeCEIDCVLBJQW/WEkHbsdu3lu83Os2LMiZHg4WjYd3cSGwxu4eejNvD/5fa4bcp3uHAIYyy4tES0dxneXCoWiw/TJ6sO/LvoXPdJ7ANq2lq0NWa311DLnszkMO36Y1nHc7xIm9p5Ihi0jFllWRIlO/aRgtVrjnYWIobToD6PpKMgoQAjB/sr9FC0tarTVZ0MtlS7/JDKznQpXBbUebaKa1Ww1hEMwml2aI1o6OnWfgkKhOBan18ncz+by9q63GZI3hKM1Rzlcc5j85Hx6ZvRkW+k23p70Nvkp+TGddKaILKpPIQSJstkGKC16xKg6Alt9Tuw1kS3FWzhUcwiJ5EjtEdYfXk9hfiEWk9bybESHYFS7NEVtshMFEmWzDVBa9IiRdQgh2HR0U8iw3Y7dZNuzY5yjyGFkuzREbbKjUChiyqHqQ206r0gMOrVTyM3NjXcWIobSoj+MrqNLapc2nTcKRrdLgGjp6NROIbAUbyKgtOgPo+uYedpM7ObGs5DtZjszT5sZpxxFBqPbJUC0dHTqeQqBNc4TAaVFfxhdR1GfIgAWfrWQQ9WH6JLahZmnzQyeNypGt0uAaOno1E5BoVC0TFGfIor6FFFcXExe3rHLXygSj07dfJSZGf4mI3pHadEfiaIDlBY9Ei0dndopBLZpTASUFv2RKDpAadEj0dLRqZ1Comy2AUqLHkkUHaC06JGE22RHoVAoFPrD8GsfCSGOAt+38/I8oDiC2YknSov+SBQdoLTokY7qOEFKmd/0pOGdQkcQQqwPtSCUEVFa9Eei6AClRY9ES4dqPlIoFApFEOUUFAqFQhGkszuFZ+OdgQiitOiPRNEBSoseiYqOTt2noFAoFIrGdPYnBYVCoVA0QDkFhUKRkAghcoQQ44UQatGmNqCcgsEQQhwvhPi0hfDuQoj9Qog1/tcx45AVkUMIkSmEeE8IsVIIsVQIYQsRxyKE2NvAJkPikddwSJSCVAiRDbwD/AhYHep/YCS7xJJO4RTCKEitQoi3hRD/EUJcG8u8tQX/D/2vQGoL0YYDD0gpx/hfR2OTu/AJpyD1x3tBCPG5EOLeWOexDVwOPCKlnAAcAiaGiHMK8FoDm2yJaQ7DJJyC1B/PCHY5BbhNSvkAsAI4rZk4urcLBMuwr1sIj5hNEt4phFmQzgA2SClHAT8VQqTHJHNtxwv8DKhoIc4I4FdCiK+EEH+ITbbaTKsFqRBiMmCWUo4E+ggh+sc4j2EhpXxSSrnK/zEfOBIi2gjgAiHEl/4/r16XrG+1IDWQXT6WUq4VQpyD5uQ+DxHNKHYBeBhIDhUQaZskvFMgvIJ0DLDY//4TQJezHaWUFVJKRyvR3kPTcwYwUghxStQz1kbCLEjHUG+TlcBZMchauxFCjASypZRrQwSvA34spfwRYAV+EtPMhUmYBekYDGIXIYRA+++XAe4QUQxhFyHEOKAarQIVijFE0CYJ7xTCLEhTgQP+96XA8dHNVVT5TEpZKaX0Al8DuqzJQasFqWFsIoTIARYBzTU9bpZSHvS/X4++bdJaQWoYu0iN6cBm4KIQUXRvF3/T6u+Bu1uIFlGbJLxTCJMq6h/N0jD297JCCNFVCJECTAC+iXeGQhFGQWoIm/j/tP8AZkkpm1uY8W9CiEIhhBmYBGyKWQbbSBgFqVHscpcQ4pf+j1lAeYhoRrDL3cCTUspQ+Q8QUZvo0qBxYAP1j1yFwJ74ZSV8hBDjhBA3Nzk9F1gNrAWellJuj33OWibMgtQoNrkOre39d/4RLHOEEPObxJkH/A3YCHwupfwg1pkMhzALUqPY5VngSiHEJ4AZ2G9Qu/wYmC6EWAMMFUI8HyJORG3SaWY0CyHWSCnH+NvnBkkpH28QdgLwLvABcCYwwt/8oogCQogbgT9QXzNbDVillPc2iJMBfAp8CJyPZpPWmgEVHcA/KGMxkIT2hPkEMFXZRR/4HcNNwC+iaZNO4xRaQwjRDc3brlA/cn3gL6TGA59IKZvrZFPEGGUX/RFJmyinoFAoFIogqk9BoVAoFEGUU1AoFApFEOUUFIoI4x/r35b4IZf5UCjigXIKCkWYCCGGCyHmhDhv8x/N/lMjhRCPhZnmQLT1hgKf9bzUgqIToDqaFYowEEKcCLwB7A4RbJFSXiCEmI02YbA7UAeUAAXAdQ3HwAshXgR6oy1dEDyNVklzSiknRUeFQtE66klBoWgFIcTJwB+BfWiTAhu+JDAdQEo5Dzgb2AmMl1KeBTwHeIQQ2Q2eAjz+a2YAJVLKC4A/o01C+lmsdCkUoVBPCgpFmAgh3kFbRqAh/YFRUso9QojewIPAV8ASwIK2fEIpcBLaWjsv+Wel7kObFzPQHz/P/9ohpbwwFnoUilCo9kuFIny+AzKAb9Fq+wBDAa9/8uMC4Bkp5QohxOVAOvA2cANQSf1KlnbgGbQl3V9AW4ytG7BLSvlwjLQoFCFRTkGhCJ8laJ3CGxuc+0pKuU8IcRKQAswQQsxAK+TNwAX+eBa0p4pNQCbQC23tHSf1S7VnCyEsUkoPCkWcUM1HCkUY+NdrOg9wodX+l6DV8ucGFh30D0V9xH/+ZLSmpgOAu0lH82op5VghRJI/rV8DvwS2SSmXxE6VQnEsqqNZoQiPd4DJwB3ArcD3wDagQmikozUH2YH/NbhuHXCLEOIhIYRJCDEI/9r3Ukon2vLh64AhaIsyKhRxRT0pKBStIIRIA5ahDSH9L1rtfhfaTl1nonUWfwB8K6V8TQhR4I//eynlu/4niFuAl9A6lx1oW5Lm+NNZitaENBat2Wm2lPLDmAlUKBqgnIJCEWH8k9j6SCl3xDsvCkVbUU5BoVAoFEFUn4JCoVAogiinoFAoFIogyikoFAqFIohyCgqFQqEI8v9IuUg/KcDHLgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x0=np.array([x.mean(),x.mean()**2,x.mean()**3])\n",
    "y0=14+5.5*x0[0]+4.8*x0[1]+0.5*x0[2]\n",
    "X=x.reshape(N,1)\n",
    "Y=np.array(z)\n",
    "degree=[2,3]\n",
    "for i in range(len(degree)):\n",
    "    tmp=pow(x,degree[i]).reshape(N,1)\n",
    "    X=np.hstack((X,tmp))\n",
    "modelLR=LM.LinearRegression()\n",
    "KNNregr=neighbors.KNeighborsRegressor(n_neighbors=5)\n",
    "model1,model2,model3,model4=[],[],[],[]    \n",
    "kf = KFold(n_splits=10,shuffle=True,random_state=123)\n",
    "for train_index, test_index in kf.split(X):   \n",
    "    Ntrain=len(train_index)\n",
    "    XKtrain=X[train_index,]\n",
    "    YKtrain=Y[train_index,]\n",
    "    modelLR.fit(XKtrain[:,0].reshape(Ntrain,1),YKtrain)\n",
    "    model1.append(modelLR.predict(x0[0].reshape(1,1)))\n",
    "    modelLR.fit(XKtrain[:,0:2].reshape(Ntrain,2),YKtrain)\n",
    "    model2.append(modelLR.predict(x0[0:2].reshape(1,2)))\n",
    "    modelLR.fit(XKtrain[:,0:3].reshape(Ntrain,3),YKtrain)\n",
    "    model3.append(modelLR.predict(x0[0:3].reshape(1,3)))\n",
    "    KNNregr.fit(XKtrain[:,0].reshape(Ntrain,1),YKtrain)\n",
    "    model4.append(KNNregr.predict(x0[0].reshape(1,1)))\n",
    "\n",
    "fig,axes = plt.subplots(1,1,figsize=(6,4))\n",
    "VI=[np.var(model1)/np.mean(model1),np.var(model2)/np.mean(model2),np.var(model3)/np.mean(model3),np.var(model4)//np.mean(model4)]\n",
    "Err=[np.mean(model1)-y0,np.mean(model2)-y0,np.mean(model3)-y0,np.mean(model4)-y0]\n",
    "Err=pow(np.array(Err),2)\n",
    "\n",
    "axes.plot(np.arange(1,5),preprocessing.scale(VI),marker='o',linestyle='-',label='方差')\n",
    "axes.plot(np.arange(1,5),preprocessing.scale(Err),marker='o',linestyle='--',label='偏差')\n",
    "axes.plot(np.arange(1,5),preprocessing.scale(MSEMean),marker='o',linestyle='-.',label=\"Err\")\n",
    "axes.set_ylabel('标准化值')\n",
    "axes.set_xlabel('复杂度')\n",
    "axes.set_title('不同复杂度模型的Err以及偏差和方差的变化趋势图')\n",
    "axes.grid(linestyle=\"--\", alpha=0.3)\n",
    "plt.legend(loc='center',bbox_to_anchor=(0.5,0.8))\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "说明：\n",
    "1、对于上述模拟数据和四种复杂度模型，计算测试误差，偏差和方差，并直观展示它们之间的关系。\n",
    "2、偏差是预测值的期望与真值的差，这里的真值指定为：输入变量均值点x0的输出变量真值y0。\n",
    "3、代码中的VI是变异系数，等于方差除以均值。方差的数值大小受数量级的影响，变异系数消除了这个影响，便于对不同情况下数据离散程度大小的对比。\n",
    "4、简单模型的偏差大方差小，复杂模型的偏差小方差大。"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
